Solve Absolute Value Equations

What’s the absolute value of -3?  |-3| = 3  That was easy.

How about the absolute value of  3?  |3|=3.

Now let’s try this brain teaser, the absolute value of what number is 3?  i.e. |x|=3?   well we already determined above that 3 and -3 both have the absolute value of 3.  Therefore the solutions to |x|=3  are 3 and -3.

What’s my point?  well my point is that absolute value equations will always have two solutions.  Also we use the fact that opposite values (i.e. -3 and 3 for example) have the same absolute value.  Let’s do some creative thinking here…

Consider | x + 1 | = 3  this absolute value equation is very similar to the one above but instead of x we have x + 1 inside the absolute value symbols.   Don’t be tricked we know that the only two numbers that result in an absolute value of 3 after taking there absolute value are 3 and -3.  Therefore x + 1 must be equal to 3 or -3.  This little concept is the key to unlocking the solutions to absolute value equations…start with easy absolute value equations to see how this whole thing works!  good luck- the steps below should help a lot.

some key topics that involve solving absolute value equations:

* linear equations
* quadratic equations
* SAT and ACT exams
* college prep math and science courses

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